My view on this is: if it's not only possible, but common for a champion to be able to stack multiple shields on themselves, and not suffer any major consequences, then the environment itself is too full of shields, and needs to change. I think the biggest culprit at this point is itemization, where items like Locket massively contribute to the overall amount of shielding in the game, and on top of that enchanter supports frequently overlap with each other in how they provide shields. In the game's current state, the only way for supports to scale has been through healing and shielding power, which itself has contributed to shield creep in the game. Toning down the raw strength of many of these shields could help, but on top of that I also think many of them need a reduction in duration: many enchanter shields especially have such a high duration that they can have close to 100% uptime at max CDR, which means they end up not really providing their opponent with a window of vulnerability for them to exploit.
As a side note, I think a ton of shields just happen to be designed in a very boring manner, i.e. by mostly acting as extra health bars, when they could be vehicles for much more interesting power. Janna's E actually has this really interesting effect where the AD it provides is lost if the shield is popped: putting more emphasis on this kind of mechanic, i.e. by reducing the power of shields and giving them powerful bonuses that exist only while the shield lasts, could turn the tables on shielding, giving shielded players moments where they'd specifically want to avoid taking damage to their shields if it means keeping their combat bonuses. On the flipside, this mean that attackers could still feel rewarded for popping a champion's shields, even if they didn't do much to their health bar, because they would have severely weakened their opponent.